Find each square root. See Example 1. √4⁄25

Verified step by step guidance

1. Recognize that the expression $\sqrt{\frac{4}{25}}$ is a square root of a fraction.
2. Apply the property of square roots that states $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$.
3. Identify the numerator and denominator: $a=4$ and $b=25$.
4. Calculate the square root of the numerator: $\sqrt{4}$.
5. Calculate the square root of the denominator: $\sqrt{25}$.

Key Concepts

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, since 2 × 2 = 4. Square roots can be positive or negative, but in most contexts, the principal (non-negative) square root is used.

Fractional Square Roots

When dealing with square roots of fractions, the square root of a fraction can be found by taking the square root of the numerator and the denominator separately. For instance, √(a/b) = √a / √b. This property simplifies the process of finding square roots of fractions.

Simplifying Square Roots

Simplifying square roots involves expressing the square root in its simplest form. This can include factoring out perfect squares from under the radical. For example, √(4/25) simplifies to √4 / √25, which equals 2/5, as both 4 and 25 are perfect squares.